Question

A rifle bullet with mass 8.00 g strikes and embeds itself in a block with mass 0.992 kg that rests on a frictionless, horizontal surface and is attached to a coil spring (as shown below). The impact compresses the spring 15.0 cm. Calibration of the spring shows that a force of 0.750 N is required to compress the spring 0.250 cm.

a) Find the magnitude of the block’s velocity just after impact.

b) What was the initial speed of the bullet?

Answer 1

a)

$$k=\frac{0.75(100)}{0.25}=300\frac{N}{m}$$

$$0.5(m+M)v^2=0.5kx^2\\(0.008+0.992)v^2=(300)(0.15)^2\\v=2.60\frac{m}{s}$$

b)

$$(m+M)v=mu\\(0.008+0.992)2.6=0.008u\\u=325\frac{m}{s}$$